Dimensionality and Dance

Professor Julie Strandberg of the Program in Dance at Brown University explored freedom of movement by choreographing Dimensions, a twenty-minute piece for two dozen dancers that has had several performances in two different years at Brown University and once in New York City. As preparation for participating in this work, dancers began with a series of exercises designed to increase their appreciation of the effect on their movements of limiting their dimensionality. They lay down on their backs or stomachs or sides on the gymnasium floor and tried to wriggle along while staying in the second dimension. Standing up, tried to walk along a line ``Egyptian hieroglyphic style,'' always staying as much as possible in a vertical plane. They explored the possible motions they could make with their backs up against a wall--for example, they might be able to do cartwheels but not somersaults. For one dancer to pass to the other side of a fellow dancer while remaining flat against the wall is an athletic challenge.

In the actual performance, the trained dancers eventually leave the confines of the wall, first to move in increasingly complicated ways while maintaining contact with the dimensional stage, and ultimately moving beyond the limitations of gravity with leaps and lifts and movement on swings. The dance tells the story of a Flatlander who is suddenly introduced to the world of three dimensions. The contrast between the extremely constricted movement of even the most imaginative Flatlanders and the freedom of motion of the Spaceland dancers is striking. The sole Flatlander to be given a glimpse of this higher-dimensional paradise is entranced by the movement of a pair of dancers, whom she joins by inserting herself, like a playing card, between them until they help her to move in space by herself. There is a real sense of liberation, heightened by the use of color and intricate rhythms to accompany the twists and turns and leaps and lifts that are not possible in the planar environment. As it happens, the experience is too much for her, and all too soon she plummets back to her Flatland plane, racked by the memory of that freer, higher-dimensional land. It is a sad tale, but a magnificent parable.

The configuration space of all possible dance positions has extremely high dimensionality. The position of the left upper arm relative to the shoulders is already three-dimensional, determined by the same sort of angles that are measured with a goniometer in the analysis of the lower back. The position of the lower arm, rotated and twisted relative to the upper, adds another three dimensions. We have six dimensions for the left arm and we have not even reached the wrist! Only when we record and analyze such configurations do we begin to realize the dimensionality of the world we move through without thinking.

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